Details

analyze1.0s (8.6%)

Algorithm

1×	search
2×	egg-herbie

Rules

12×	`*-commutative_binary64_1373`
4×	`distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391` `associate-/l*_binary64_1387` `+-commutative_binary64_1372`
2×	`associate-/r/_binary64_1388` `associate-l/_binary64_1385` `associate-r/_binary64_1384` `associate-l_binary64_1383` `associate-r_binary64_1382`
1×	`1-exp_binary64_1486`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_1705` `erf-erfc_binary64_1704` `erf-odd_binary64_1703` `if-if-and-not_binary64_1702` `if-if-and_binary64_1701` `if-if-or-not_binary64_1700` `if-if-or_binary64_1699` `if-not_binary64_1698` `if-same_binary64_1697` `if-false_binary64_1696` `if-true_binary64_1695` `not-gte_binary64_1694` `not-lte_binary64_1693` `not-gt_binary64_1692` `not-lt_binary64_1691` `gte-same_binary64_1690` `lte-same_binary64_1689` `gt-same_binary64_1688` `lt-same_binary64_1687` `sinh---cosh_binary64_1634` `sinh-+-cosh_binary64_1633` `sinh-cosh_binary64_1632` `tanh-def-c_binary64_1631` `tanh-def-b_binary64_1630` `tanh-def-a_binary64_1629` `cosh-def_binary64_1628` `sinh-def_binary64_1627` `tan-neg_binary64_1574` `cos-neg_binary64_1573` `sin-neg_binary64_1572` `tan-0_binary64_1571` `cos-0_binary64_1570` `sin-0_binary64_1569` `hang-m-tan_binary64_1568` `hang-p-tan_binary64_1567` `hang-m0-tan_binary64_1566` `hang-p0-tan_binary64_1565` `hang-0m-tan_binary64_1564` `hang-0p-tan_binary64_1563` `tan-+PI/2_binary64_1562` `tan-+PI_binary64_1561` `tan-PI_binary64_1560` `tan-PI/3_binary64_1559` `tan-PI/4_binary64_1558` `tan-PI/6_binary64_1557` `cos-+PI/2_binary64_1556` `cos-+PI_binary64_1555` `cos-PI_binary64_1554` `cos-PI/2_binary64_1553` `cos-PI/3_binary64_1552` `cos-PI/4_binary64_1551` `cos-PI/6_binary64_1550` `sin-+PI/2_binary64_1549` `sin-+PI_binary64_1548` `sin-PI_binary64_1547` `sin-PI/2_binary64_1546` `sin-PI/3_binary64_1545` `sin-PI/4_binary64_1544` `sin-PI/6_binary64_1543` `sub-1-sin_binary64_1542` `sub-1-cos_binary64_1541` `-1-add-sin_binary64_1540` `-1-add-cos_binary64_1539` `1-sub-sin_binary64_1538` `1-sub-cos_binary64_1537` `cos-sin-sum_binary64_1536` `log-E_binary64_1532` `log-pow_binary64_1531` `log-rec_binary64_1530` `log-div_binary64_1529` `log-prod_binary64_1528` `pow-base-0_binary64_1526` `unpow1/3_binary64_1509` `unpow3_binary64_1508` `unpow2_binary64_1507` `unpow1/2_binary64_1506` `pow-plus_binary64_1505` `exp-to-pow_binary64_1504` `pow-base-1_binary64_1502` `unpow0_binary64_1501` `unpow1_binary64_1500` `unpow-1_binary64_1499` `exp-lft-cube_binary64_1498` `exp-lft-sqr_binary64_1497` `exp-cbrt_binary64_1496` `exp-sqrt_binary64_1495` `exp-prod_binary64_1494` `div-exp_binary64_1493` `rec-exp_binary64_1492` `prod-exp_binary64_1491` `exp-diff_binary64_1490` `exp-neg_binary64_1489` `exp-sum_binary64_1488` `e-exp-1_binary64_1487` `exp-1-e_binary64_1485` `exp-0_binary64_1484` `rem-log-exp_binary64_1483` `rem-exp-log_binary64_1482` `cube-unmult_binary64_1479` `cube-mult_binary64_1472` `cube-div_binary64_1471` `cube-prod_binary64_1470` `cube-neg_binary64_1469` `rem-3cbrt-rft_binary64_1468` `rem-3cbrt-lft_binary64_1467` `rem-cbrt-cube_binary64_1466` `rem-cube-cbrt_binary64_1465` `sqr-abs_binary64_1457` `sqr-neg_binary64_1456` `rem-sqrt-square_binary64_1455` `rem-square-sqrt_binary64_1454` `times-frac_binary64_1448` `div-sub_binary64_1447` `neg-mul-1_binary64_1438` `neg-sub0_binary64_1437` `unsub-neg_binary64_1436` `sub-neg_binary64_1435` `mul-1-neg_binary64_1434` `/-rgt-identity_binary64_1433` `-rgt-identity_binary64_1432` `-lft-identity_binary64_1431` `remove-double-neg_binary64_1430` `sub0-neg_binary64_1429` `--rgt-identity_binary64_1428` `+-rgt-identity_binary64_1427` `+-lft-identity_binary64_1426` `mul0-rgt_binary64_1425` `mul0-lft_binary64_1424` `div0_binary64_1423` `-inverses_binary64_1422` `+-inverses_binary64_1421` `lft-mult-inverse_binary64_1420` `rgt-mult-inverse_binary64_1419` `remove-double-div_binary64_1418` `pow-sqr_binary64_1415` `sqr-pow_binary64_1414` `difference-of-sqr--1_binary64_1413` `difference-of-sqr-1_binary64_1412` `difference-of-squares_binary64_1411` `unswap-sqr_binary64_1410` `swap-sqr_binary64_1409` `cancel-sign-sub-inv_binary64_1408` `cancel-sign-sub_binary64_1407` `distribute-neg-frac_binary64_1406` `distribute-frac-neg_binary64_1405` `distribute-neg-out_binary64_1404` `distribute-neg-in_binary64_1403` `distribute-rgt-neg-out_binary64_1402` `distribute-lft-neg-out_binary64_1401` `distribute-rgt-neg-in_binary64_1400` `distribute-lft-neg-in_binary64_1399` `distribute-rgt1-in_binary64_1398` `distribute-lft1-in_binary64_1397` `distribute-rgt-out--_binary64_1396` `distribute-rgt-out_binary64_1395` `distribute-lft-out--_binary64_1394` `distribute-lft-out_binary64_1393` `count-2_binary64_1390` `associate-/l/_binary64_1389` `associate-/r_binary64_1386` `associate--r-_binary64_1381` `associate--l-_binary64_1380` `associate--l+_binary64_1379` `associate--r+_binary64_1378` `associate-+l-_binary64_1377` `associate-+r-_binary64_1376` `associate-+l+_binary64_1375` `associate-+r+_binary64_1374`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	52
1	48	52
2	58	52
3	64	52
4	68	52
5	70	52
6	67	52
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

Compiler

Compiled 22 to 18 computations (18.2% saved)

sample42.0ms (0.4%)

Algorithm

1×

intervals

Results

12.0ms	205×	body	128	valid
6.0ms	21×	body	2048	valid
5.0ms	256×	pre	128	true
3.0ms	15×	body	1024	valid
1.0ms	4×	body	4096	valid
1.0ms	7×	body	512	valid
0.0ms	4×	body	256	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64_1373`
2×	`distribute-rgt-in_binary64_1392` `distribute-lft-in_binary64_1391` `associate-/l*_binary64_1387` `+-commutative_binary64_1372`
1×	`1-exp_binary64_1486` `associate-/r/_binary64_1388` `associate-l/_binary64_1385` `associate-r/_binary64_1384` `associate-l_binary64_1383` `associate-r_binary64_1382`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_1705` `erf-erfc_binary64_1704` `erf-odd_binary64_1703` `if-if-and-not_binary64_1702` `if-if-and_binary64_1701` `if-if-or-not_binary64_1700` `if-if-or_binary64_1699` `if-not_binary64_1698` `if-same_binary64_1697` `if-false_binary64_1696` `if-true_binary64_1695` `not-gte_binary64_1694` `not-lte_binary64_1693` `not-gt_binary64_1692` `not-lt_binary64_1691` `gte-same_binary64_1690` `lte-same_binary64_1689` `gt-same_binary64_1688` `lt-same_binary64_1687` `sinh---cosh_binary64_1634` `sinh-+-cosh_binary64_1633` `sinh-cosh_binary64_1632` `tanh-def-c_binary64_1631` `tanh-def-b_binary64_1630` `tanh-def-a_binary64_1629` `cosh-def_binary64_1628` `sinh-def_binary64_1627` `tan-neg_binary64_1574` `cos-neg_binary64_1573` `sin-neg_binary64_1572` `tan-0_binary64_1571` `cos-0_binary64_1570` `sin-0_binary64_1569` `hang-m-tan_binary64_1568` `hang-p-tan_binary64_1567` `hang-m0-tan_binary64_1566` `hang-p0-tan_binary64_1565` `hang-0m-tan_binary64_1564` `hang-0p-tan_binary64_1563` `tan-+PI/2_binary64_1562` `tan-+PI_binary64_1561` `tan-PI_binary64_1560` `tan-PI/3_binary64_1559` `tan-PI/4_binary64_1558` `tan-PI/6_binary64_1557` `cos-+PI/2_binary64_1556` `cos-+PI_binary64_1555` `cos-PI_binary64_1554` `cos-PI/2_binary64_1553` `cos-PI/3_binary64_1552` `cos-PI/4_binary64_1551` `cos-PI/6_binary64_1550` `sin-+PI/2_binary64_1549` `sin-+PI_binary64_1548` `sin-PI_binary64_1547` `sin-PI/2_binary64_1546` `sin-PI/3_binary64_1545` `sin-PI/4_binary64_1544` `sin-PI/6_binary64_1543` `sub-1-sin_binary64_1542` `sub-1-cos_binary64_1541` `-1-add-sin_binary64_1540` `-1-add-cos_binary64_1539` `1-sub-sin_binary64_1538` `1-sub-cos_binary64_1537` `cos-sin-sum_binary64_1536` `log-E_binary64_1532` `log-pow_binary64_1531` `log-rec_binary64_1530` `log-div_binary64_1529` `log-prod_binary64_1528` `pow-base-0_binary64_1526` `unpow1/3_binary64_1509` `unpow3_binary64_1508` `unpow2_binary64_1507` `unpow1/2_binary64_1506` `pow-plus_binary64_1505` `exp-to-pow_binary64_1504` `pow-base-1_binary64_1502` `unpow0_binary64_1501` `unpow1_binary64_1500` `unpow-1_binary64_1499` `exp-lft-cube_binary64_1498` `exp-lft-sqr_binary64_1497` `exp-cbrt_binary64_1496` `exp-sqrt_binary64_1495` `exp-prod_binary64_1494` `div-exp_binary64_1493` `rec-exp_binary64_1492` `prod-exp_binary64_1491` `exp-diff_binary64_1490` `exp-neg_binary64_1489` `exp-sum_binary64_1488` `e-exp-1_binary64_1487` `exp-1-e_binary64_1485` `exp-0_binary64_1484` `rem-log-exp_binary64_1483` `rem-exp-log_binary64_1482` `cube-unmult_binary64_1479` `cube-mult_binary64_1472` `cube-div_binary64_1471` `cube-prod_binary64_1470` `cube-neg_binary64_1469` `rem-3cbrt-rft_binary64_1468` `rem-3cbrt-lft_binary64_1467` `rem-cbrt-cube_binary64_1466` `rem-cube-cbrt_binary64_1465` `sqr-abs_binary64_1457` `sqr-neg_binary64_1456` `rem-sqrt-square_binary64_1455` `rem-square-sqrt_binary64_1454` `times-frac_binary64_1448` `div-sub_binary64_1447` `neg-mul-1_binary64_1438` `neg-sub0_binary64_1437` `unsub-neg_binary64_1436` `sub-neg_binary64_1435` `mul-1-neg_binary64_1434` `/-rgt-identity_binary64_1433` `-rgt-identity_binary64_1432` `-lft-identity_binary64_1431` `remove-double-neg_binary64_1430` `sub0-neg_binary64_1429` `--rgt-identity_binary64_1428` `+-rgt-identity_binary64_1427` `+-lft-identity_binary64_1426` `mul0-rgt_binary64_1425` `mul0-lft_binary64_1424` `div0_binary64_1423` `-inverses_binary64_1422` `+-inverses_binary64_1421` `lft-mult-inverse_binary64_1420` `rgt-mult-inverse_binary64_1419` `remove-double-div_binary64_1418` `pow-sqr_binary64_1415` `sqr-pow_binary64_1414` `difference-of-sqr--1_binary64_1413` `difference-of-sqr-1_binary64_1412` `difference-of-squares_binary64_1411` `unswap-sqr_binary64_1410` `swap-sqr_binary64_1409` `cancel-sign-sub-inv_binary64_1408` `cancel-sign-sub_binary64_1407` `distribute-neg-frac_binary64_1406` `distribute-frac-neg_binary64_1405` `distribute-neg-out_binary64_1404` `distribute-neg-in_binary64_1403` `distribute-rgt-neg-out_binary64_1402` `distribute-lft-neg-out_binary64_1401` `distribute-rgt-neg-in_binary64_1400` `distribute-lft-neg-in_binary64_1399` `distribute-rgt1-in_binary64_1398` `distribute-lft1-in_binary64_1397` `distribute-rgt-out--_binary64_1396` `distribute-rgt-out_binary64_1395` `distribute-lft-out--_binary64_1394` `distribute-lft-out_binary64_1393` `count-2_binary64_1390` `associate-/l/_binary64_1389` `associate-/r_binary64_1386` `associate--r-_binary64_1381` `associate--l-_binary64_1380` `associate--l+_binary64_1379` `associate--r+_binary64_1378` `associate-+l-_binary64_1377` `associate-+r-_binary64_1376` `associate-+l+_binary64_1375` `associate-+r+_binary64_1374`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	30	26
2	35	26
3	38	26
4	40	26
5	41	26
6	38	26

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

11.7b

Counts

2 → 1

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))
0.0b	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
0.7b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
13.3b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite192.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

11.5b

Rules

22×	`*-un-lft-identity_binary64_1442`
21×	`add-sqr-sqrt_binary64_1464`
20×	`add-cube-cbrt_binary64_1477`
18×	`times-frac_binary64_1448`
15×	`sqrt-prod_binary64_1458`
8×	`add-log-exp_binary64_1481`
6×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `associate-/r*_binary64_1386`
5×	`pow1_binary64_1503`
4×	`flip3-+_binary64_1445` `sqrt-div_binary64_1459` `flip-+_binary64_1416`
3×	`associate-/l*_binary64_1387`
2×	`sum-log_binary64_1533` `+-commutative_binary64_1372` `associate-/r/_binary64_1388`
1×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `distribute-lft-out_binary64_1393` `div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `div-inv_binary64_1439`

Counts

4 → 79

Calls

4 calls:

18.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
9.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
6.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))
6.0ms	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))

Compiler

Compiled 2389 to 1490 computations (37.6% saved)

series974.0ms (8.3%)

Error

5.9b

Counts

4 → 66

Calls

4 calls:

302.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
227.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
184.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))
184.0ms	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))

Compiler

Compiled 2772 to 2413 computations (13% saved)

simplify127.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

571×	`associate-l_binary64_1383`
516×	`times-frac_binary64_1448`
406×	`associate-/l*_binary64_1387`
274×	`associate-/r*_binary64_1386`
207×	`cancel-sign-sub-inv_binary64_1408`
182×	`associate-*l/_binary64_1385`
172×	`associate-*r/_binary64_1384`
133×	`distribute-rgt-neg-in_binary64_1400`
122×	`neg-sub0_binary64_1437`
121×	`neg-mul-1_binary64_1438`
119×	`distribute-lft-neg-in_binary64_1399`
106×	`distribute-rgt-in_binary64_1392`
84×	`associate-/l/_binary64_1389`
82×	`distribute-lft-in_binary64_1391` `associate-/r/_binary64_1388`
76×	`distribute-neg-frac_binary64_1406`
74×	`associate-r_binary64_1382`
72×	`sub-neg_binary64_1435`
65×	`unswap-sqr_binary64_1410`
56×	`div-sub_binary64_1447`
53×	`+-commutative_binary64_1372`
52×	`*-commutative_binary64_1373`
50×	`sqr-pow_binary64_1414`
30×	`exp-prod_binary64_1494`
29×	`cube-prod_binary64_1470`
23×	`associate--l+_binary64_1379`
17×	`cube-div_binary64_1471`
15×	`log-div_binary64_1529` `cube-unmult_binary64_1479` `distribute-rgt-out_binary64_1395` `distribute-lft-out_binary64_1393`
14×	`log-prod_binary64_1528`
13×	`pow-plus_binary64_1505`
11×	`unpow3_binary64_1508` `*-rgt-identity_binary64_1432` `distribute-rgt-out--_binary64_1396` `associate-+l+_binary64_1375`
10×	`swap-sqr_binary64_1409`
8×	`cube-mult_binary64_1472` `distribute-lft-neg-out_binary64_1401` `distribute-lft-out--_binary64_1394`
7×	`unsub-neg_binary64_1436` `associate--r+_binary64_1378`
6×	`*-lft-identity_binary64_1431` `distribute-neg-in_binary64_1403`
5×	`distribute-rgt1-in_binary64_1398`
4×	`unpow2_binary64_1507` `rem-sqrt-square_binary64_1455` `/-rgt-identity_binary64_1433` `associate-+r+_binary64_1374`
3×	`unpow1/2_binary64_1506` `pow-sqr_binary64_1415` `associate-+l-_binary64_1377` `associate-+r-_binary64_1376`
2×	`log-pow_binary64_1531` `log-rec_binary64_1530` `unpow1_binary64_1500` `prod-exp_binary64_1491`
1×	`exp-sum_binary64_1488` `1-exp_binary64_1486` `exp-1-e_binary64_1485` `rem-square-sqrt_binary64_1454` `sub0-neg_binary64_1429` `+-rgt-identity_binary64_1427` `difference-of-squares_binary64_1411` `distribute-rgt-neg-out_binary64_1402` `count-2_binary64_1390`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_1705` `erf-erfc_binary64_1704` `erf-odd_binary64_1703` `if-if-and-not_binary64_1702` `if-if-and_binary64_1701` `if-if-or-not_binary64_1700` `if-if-or_binary64_1699` `if-not_binary64_1698` `if-same_binary64_1697` `if-false_binary64_1696` `if-true_binary64_1695` `not-gte_binary64_1694` `not-lte_binary64_1693` `not-gt_binary64_1692` `not-lt_binary64_1691` `gte-same_binary64_1690` `lte-same_binary64_1689` `gt-same_binary64_1688` `lt-same_binary64_1687` `sinh---cosh_binary64_1634` `sinh-+-cosh_binary64_1633` `sinh-cosh_binary64_1632` `tanh-def-c_binary64_1631` `tanh-def-b_binary64_1630` `tanh-def-a_binary64_1629` `cosh-def_binary64_1628` `sinh-def_binary64_1627` `tan-neg_binary64_1574` `cos-neg_binary64_1573` `sin-neg_binary64_1572` `tan-0_binary64_1571` `cos-0_binary64_1570` `sin-0_binary64_1569` `hang-m-tan_binary64_1568` `hang-p-tan_binary64_1567` `hang-m0-tan_binary64_1566` `hang-p0-tan_binary64_1565` `hang-0m-tan_binary64_1564` `hang-0p-tan_binary64_1563` `tan-+PI/2_binary64_1562` `tan-+PI_binary64_1561` `tan-PI_binary64_1560` `tan-PI/3_binary64_1559` `tan-PI/4_binary64_1558` `tan-PI/6_binary64_1557` `cos-+PI/2_binary64_1556` `cos-+PI_binary64_1555` `cos-PI_binary64_1554` `cos-PI/2_binary64_1553` `cos-PI/3_binary64_1552` `cos-PI/4_binary64_1551` `cos-PI/6_binary64_1550` `sin-+PI/2_binary64_1549` `sin-+PI_binary64_1548` `sin-PI_binary64_1547` `sin-PI/2_binary64_1546` `sin-PI/3_binary64_1545` `sin-PI/4_binary64_1544` `sin-PI/6_binary64_1543` `sub-1-sin_binary64_1542` `sub-1-cos_binary64_1541` `-1-add-sin_binary64_1540` `-1-add-cos_binary64_1539` `1-sub-sin_binary64_1538` `1-sub-cos_binary64_1537` `cos-sin-sum_binary64_1536` `log-E_binary64_1532` `pow-base-0_binary64_1526` `unpow1/3_binary64_1509` `exp-to-pow_binary64_1504` `pow-base-1_binary64_1502` `unpow0_binary64_1501` `unpow-1_binary64_1499` `exp-lft-cube_binary64_1498` `exp-lft-sqr_binary64_1497` `exp-cbrt_binary64_1496` `exp-sqrt_binary64_1495` `div-exp_binary64_1493` `rec-exp_binary64_1492` `exp-diff_binary64_1490` `exp-neg_binary64_1489` `e-exp-1_binary64_1487` `exp-0_binary64_1484` `rem-log-exp_binary64_1483` `rem-exp-log_binary64_1482` `cube-neg_binary64_1469` `rem-3cbrt-rft_binary64_1468` `rem-3cbrt-lft_binary64_1467` `rem-cbrt-cube_binary64_1466` `rem-cube-cbrt_binary64_1465` `sqr-abs_binary64_1457` `sqr-neg_binary64_1456` `mul-1-neg_binary64_1434` `remove-double-neg_binary64_1430` `--rgt-identity_binary64_1428` `+-lft-identity_binary64_1426` `mul0-rgt_binary64_1425` `mul0-lft_binary64_1424` `div0_binary64_1423` `*-inverses_binary64_1422` `+-inverses_binary64_1421` `lft-mult-inverse_binary64_1420` `rgt-mult-inverse_binary64_1419` `remove-double-div_binary64_1418` `difference-of-sqr--1_binary64_1413` `difference-of-sqr-1_binary64_1412` `cancel-sign-sub_binary64_1407` `distribute-frac-neg_binary64_1405` `distribute-neg-out_binary64_1404` `distribute-lft1-in_binary64_1397` `associate--r-_binary64_1381` `associate--l-_binary64_1380`

Counts

145 → 118

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	189	3247
1	478	3089
2	1337	3086
3	4737	3059
4	4966	3059

prune171.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	115	3	118
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	115	4	119

Error

4.7b

Counts

119 → 4

Compiler

Compiled 2946 to 1781 computations (39.5% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))))
13.3b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))
13.3b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))
13.3b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))

rewrite200.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

4.7b

Rules

10×	`add-sqr-sqrt_binary64_1464`
9×	`sqrt-prod_binary64_1458` `*-un-lft-identity_binary64_1442`
7×	`pow1_binary64_1503` `add-cube-cbrt_binary64_1477`
6×	`add-log-exp_binary64_1481` `sqrt-div_binary64_1459`
4×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `flip3-+_binary64_1445` `flip-+_binary64_1416`
3×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455`
1×	`sum-log_binary64_1533` `distribute-lft-out_binary64_1393` `+-commutative_binary64_1372`

Counts

4 → 57

Calls

4 calls:

15.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))))
5.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))

Compiler

Compiled 3533 to 2031 computations (42.5% saved)

series1.1s (9.3%)

Error

4.7b

Counts

4 → 75

Calls

4 calls:

263.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))))
222.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))
212.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))
199.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))

Compiler

Compiled 8746 to 6087 computations (30.4% saved)

simplify113.0ms (1%)

Algorithm

1×	egg-herbie

Rules

444×	`times-frac_binary64_1448`
391×	`associate-r_binary64_1382`
380×	`associate-l_binary64_1383`
323×	`unswap-sqr_binary64_1410`
299×	`associate-/l*_binary64_1387`
230×	`associate-/r*_binary64_1386`
168×	`cancel-sign-sub-inv_binary64_1408`
157×	`sub-neg_binary64_1435`
142×	`distribute-rgt-neg-in_binary64_1400`
141×	`associate-*l/_binary64_1385`
128×	`associate-*r/_binary64_1384`
126×	`distribute-lft-neg-in_binary64_1399`
124×	`*-commutative_binary64_1373`
112×	`neg-sub0_binary64_1437`
107×	`neg-mul-1_binary64_1438`
71×	`+-commutative_binary64_1372`
68×	`distribute-neg-frac_binary64_1406`
59×	`sqr-pow_binary64_1414`
53×	`div-sub_binary64_1447`
45×	`distribute-rgt-in_binary64_1392`
39×	`associate-+l+_binary64_1375`
33×	`associate-/r/_binary64_1388` `associate-+r+_binary64_1374`
32×	`associate-+l-_binary64_1377`
30×	`distribute-lft-in_binary64_1391` `associate-+r-_binary64_1376`
28×	`+-rgt-identity_binary64_1427`
26×	`cube-prod_binary64_1470`
25×	`associate--l+_binary64_1379`
23×	`/-rgt-identity_binary64_1433`
19×	`sub0-neg_binary64_1429`
17×	`unsub-neg_binary64_1436`
14×	`cube-unmult_binary64_1479`
12×	`*-lft-identity_binary64_1431` `distribute-lft-neg-out_binary64_1401`
11×	`unpow3_binary64_1508` `distribute-rgt-out--_binary64_1396`
10×	`pow-plus_binary64_1505` `cube-div_binary64_1471`
8×	`cube-mult_binary64_1472` `*-rgt-identity_binary64_1432` `difference-of-squares_binary64_1411` `swap-sqr_binary64_1409` `distribute-rgt-out_binary64_1395`
7×	`associate-/l/_binary64_1389`
6×	`associate--r+_binary64_1378`
5×	`distribute-rgt1-in_binary64_1398`
4×	`exp-prod_binary64_1494` `rem-sqrt-square_binary64_1455` `pow-sqr_binary64_1415` `distribute-neg-in_binary64_1403`
3×	`unpow1/2_binary64_1506` `distribute-lft-out--_binary64_1394`
2×	`log-prod_binary64_1528` `unpow2_binary64_1507` `unpow1_binary64_1500`
1×	`prod-exp_binary64_1491` `1-exp_binary64_1486` `exp-1-e_binary64_1485` `rem-square-sqrt_binary64_1454` `mul-1-neg_binary64_1434` `div0_binary64_1423` `difference-of-sqr-1_binary64_1412` `distribute-rgt-neg-out_binary64_1402` `distribute-lft-out_binary64_1393`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_1705` `erf-erfc_binary64_1704` `erf-odd_binary64_1703` `if-if-and-not_binary64_1702` `if-if-and_binary64_1701` `if-if-or-not_binary64_1700` `if-if-or_binary64_1699` `if-not_binary64_1698` `if-same_binary64_1697` `if-false_binary64_1696` `if-true_binary64_1695` `not-gte_binary64_1694` `not-lte_binary64_1693` `not-gt_binary64_1692` `not-lt_binary64_1691` `gte-same_binary64_1690` `lte-same_binary64_1689` `gt-same_binary64_1688` `lt-same_binary64_1687` `sinh---cosh_binary64_1634` `sinh-+-cosh_binary64_1633` `sinh-cosh_binary64_1632` `tanh-def-c_binary64_1631` `tanh-def-b_binary64_1630` `tanh-def-a_binary64_1629` `cosh-def_binary64_1628` `sinh-def_binary64_1627` `tan-neg_binary64_1574` `cos-neg_binary64_1573` `sin-neg_binary64_1572` `tan-0_binary64_1571` `cos-0_binary64_1570` `sin-0_binary64_1569` `hang-m-tan_binary64_1568` `hang-p-tan_binary64_1567` `hang-m0-tan_binary64_1566` `hang-p0-tan_binary64_1565` `hang-0m-tan_binary64_1564` `hang-0p-tan_binary64_1563` `tan-+PI/2_binary64_1562` `tan-+PI_binary64_1561` `tan-PI_binary64_1560` `tan-PI/3_binary64_1559` `tan-PI/4_binary64_1558` `tan-PI/6_binary64_1557` `cos-+PI/2_binary64_1556` `cos-+PI_binary64_1555` `cos-PI_binary64_1554` `cos-PI/2_binary64_1553` `cos-PI/3_binary64_1552` `cos-PI/4_binary64_1551` `cos-PI/6_binary64_1550` `sin-+PI/2_binary64_1549` `sin-+PI_binary64_1548` `sin-PI_binary64_1547` `sin-PI/2_binary64_1546` `sin-PI/3_binary64_1545` `sin-PI/4_binary64_1544` `sin-PI/6_binary64_1543` `sub-1-sin_binary64_1542` `sub-1-cos_binary64_1541` `-1-add-sin_binary64_1540` `-1-add-cos_binary64_1539` `1-sub-sin_binary64_1538` `1-sub-cos_binary64_1537` `cos-sin-sum_binary64_1536` `log-E_binary64_1532` `log-pow_binary64_1531` `log-rec_binary64_1530` `log-div_binary64_1529` `pow-base-0_binary64_1526` `unpow1/3_binary64_1509` `exp-to-pow_binary64_1504` `pow-base-1_binary64_1502` `unpow0_binary64_1501` `unpow-1_binary64_1499` `exp-lft-cube_binary64_1498` `exp-lft-sqr_binary64_1497` `exp-cbrt_binary64_1496` `exp-sqrt_binary64_1495` `div-exp_binary64_1493` `rec-exp_binary64_1492` `exp-diff_binary64_1490` `exp-neg_binary64_1489` `exp-sum_binary64_1488` `e-exp-1_binary64_1487` `exp-0_binary64_1484` `rem-log-exp_binary64_1483` `rem-exp-log_binary64_1482` `cube-neg_binary64_1469` `rem-3cbrt-rft_binary64_1468` `rem-3cbrt-lft_binary64_1467` `rem-cbrt-cube_binary64_1466` `rem-cube-cbrt_binary64_1465` `sqr-abs_binary64_1457` `sqr-neg_binary64_1456` `remove-double-neg_binary64_1430` `--rgt-identity_binary64_1428` `+-lft-identity_binary64_1426` `mul0-rgt_binary64_1425` `mul0-lft_binary64_1424` `*-inverses_binary64_1422` `+-inverses_binary64_1421` `lft-mult-inverse_binary64_1420` `rgt-mult-inverse_binary64_1419` `remove-double-div_binary64_1418` `difference-of-sqr--1_binary64_1413` `cancel-sign-sub_binary64_1407` `distribute-frac-neg_binary64_1405` `distribute-neg-out_binary64_1404` `distribute-lft1-in_binary64_1397` `count-2_binary64_1390` `associate--r-_binary64_1381` `associate--l-_binary64_1380`

Counts

132 → 99

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	123	2684
1	355	2575
2	1003	2536
3	4293	2524
4	4964	2524

prune291.0ms (2.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	99	4	103

Error

4.7b

Counts

103 → 4

Compiler

Compiled 5730 to 3441 computations (39.9% saved)

localize34.0ms (0.3%)

Local error

Found 4 expressions with local error:

13.3b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 4 (*.f64 p p))))
13.3b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))
13.3b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))
27.4b	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 4 (*.f64 p p)))) 3))

rewrite277.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

4.7b

Rules

18×	`cbrt-prod_binary64_1473`
15×	`add-sqr-sqrt_binary64_1464` `sqrt-prod_binary64_1458`
12×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
8×	`sqrt-div_binary64_1459`
7×	`pow1_binary64_1503`
6×	`unpow-prod-down_binary64_1521` `cube-prod_binary64_1470`
4×	`add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `flip3-+_binary64_1445` `flip-+_binary64_1416`
3×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455`
2×	`cube-div_binary64_1471` `cbrt-div_binary64_1474`
1×	`pow1/3_binary64_1524` `unpow3_binary64_1508` `cube-mult_binary64_1472` `sqr-pow_binary64_1414` `rem-cbrt-cube_binary64_1466`

Counts

4 → 74

Calls

4 calls:

7.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 4 (*.f64 p p)))) 3))
5.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 4 (*.f64 p p))))
5.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))

Compiler

Compiled 4881 to 2910 computations (40.4% saved)

series1.1s (9.5%)

Error

4.7b

Counts

4 → 76

Calls

4 calls:

232.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 4 (*.f64 p p))))
229.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))
222.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 4 (*.f64 p p)))) 3))
207.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))

Compiler

Compiled 9426 to 6665 computations (29.3% saved)

simplify150.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

581×	`associate-l_binary64_1383`
487×	`associate-r_binary64_1382`
408×	`distribute-rgt-neg-in_binary64_1400`
378×	`distribute-lft-neg-in_binary64_1399`
235×	`times-frac_binary64_1448`
223×	`distribute-neg-frac_binary64_1406`
174×	`associate-/l*_binary64_1387`
151×	`div-sub_binary64_1447`
127×	`cancel-sign-sub-inv_binary64_1408`
112×	`associate-/r*_binary64_1386`
111×	`*-commutative_binary64_1373`
102×	`sub-neg_binary64_1435` `unswap-sqr_binary64_1410`
99×	`sqr-pow_binary64_1414`
80×	`neg-sub0_binary64_1437`
74×	`neg-mul-1_binary64_1438`
61×	`associate-*l/_binary64_1385`
58×	`cube-prod_binary64_1470`
52×	`distribute-lft-neg-out_binary64_1401`
48×	`associate-*r/_binary64_1384`
47×	`unpow3_binary64_1508`
42×	`distribute-rgt-in_binary64_1392` `+-commutative_binary64_1372`
36×	`distribute-lft-in_binary64_1391`
35×	`rem-sqrt-square_binary64_1455`
33×	`pow-plus_binary64_1505`
32×	`distribute-rgt-neg-out_binary64_1402`
27×	`cube-mult_binary64_1472`
23×	`cube-unmult_binary64_1479`
21×	`associate-+r-_binary64_1376`
19×	`log-prod_binary64_1528` `+-rgt-identity_binary64_1427` `associate-+l-_binary64_1377`
18×	`exp-prod_binary64_1494` `swap-sqr_binary64_1409`
17×	`distribute-rgt-out--_binary64_1396` `associate-+l+_binary64_1375`
15×	`associate-/r/_binary64_1388`
13×	`unsub-neg_binary64_1436` `associate--l+_binary64_1379` `associate-+r+_binary64_1374`
11×	`sub0-neg_binary64_1429` `pow-sqr_binary64_1415` `distribute-neg-in_binary64_1403`
10×	`rem-cbrt-cube_binary64_1466` `distribute-rgt-out_binary64_1395`
9×	`difference-of-squares_binary64_1411`
8×	`rem-square-sqrt_binary64_1454`
5×	`log-pow_binary64_1531` `associate--r+_binary64_1378`
4×	`unpow2_binary64_1507` `cancel-sign-sub_binary64_1407`
3×	`distribute-lft-out--_binary64_1394`
2×	`unpow1/2_binary64_1506` `unpow1_binary64_1500` `cube-div_binary64_1471` `distribute-frac-neg_binary64_1405` `distribute-neg-out_binary64_1404`
1×	`1-exp_binary64_1486` `rem-3cbrt-lft_binary64_1467` `rem-cube-cbrt_binary64_1465` `sqr-abs_binary64_1457` `mul-1-neg_binary64_1434` `distribute-lft-out_binary64_1393` `count-2_binary64_1390`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_1705` `erf-erfc_binary64_1704` `erf-odd_binary64_1703` `if-if-and-not_binary64_1702` `if-if-and_binary64_1701` `if-if-or-not_binary64_1700` `if-if-or_binary64_1699` `if-not_binary64_1698` `if-same_binary64_1697` `if-false_binary64_1696` `if-true_binary64_1695` `not-gte_binary64_1694` `not-lte_binary64_1693` `not-gt_binary64_1692` `not-lt_binary64_1691` `gte-same_binary64_1690` `lte-same_binary64_1689` `gt-same_binary64_1688` `lt-same_binary64_1687` `sinh---cosh_binary64_1634` `sinh-+-cosh_binary64_1633` `sinh-cosh_binary64_1632` `tanh-def-c_binary64_1631` `tanh-def-b_binary64_1630` `tanh-def-a_binary64_1629` `cosh-def_binary64_1628` `sinh-def_binary64_1627` `tan-neg_binary64_1574` `cos-neg_binary64_1573` `sin-neg_binary64_1572` `tan-0_binary64_1571` `cos-0_binary64_1570` `sin-0_binary64_1569` `hang-m-tan_binary64_1568` `hang-p-tan_binary64_1567` `hang-m0-tan_binary64_1566` `hang-p0-tan_binary64_1565` `hang-0m-tan_binary64_1564` `hang-0p-tan_binary64_1563` `tan-+PI/2_binary64_1562` `tan-+PI_binary64_1561` `tan-PI_binary64_1560` `tan-PI/3_binary64_1559` `tan-PI/4_binary64_1558` `tan-PI/6_binary64_1557` `cos-+PI/2_binary64_1556` `cos-+PI_binary64_1555` `cos-PI_binary64_1554` `cos-PI/2_binary64_1553` `cos-PI/3_binary64_1552` `cos-PI/4_binary64_1551` `cos-PI/6_binary64_1550` `sin-+PI/2_binary64_1549` `sin-+PI_binary64_1548` `sin-PI_binary64_1547` `sin-PI/2_binary64_1546` `sin-PI/3_binary64_1545` `sin-PI/4_binary64_1544` `sin-PI/6_binary64_1543` `sub-1-sin_binary64_1542` `sub-1-cos_binary64_1541` `-1-add-sin_binary64_1540` `-1-add-cos_binary64_1539` `1-sub-sin_binary64_1538` `1-sub-cos_binary64_1537` `cos-sin-sum_binary64_1536` `log-E_binary64_1532` `log-rec_binary64_1530` `log-div_binary64_1529` `pow-base-0_binary64_1526` `unpow1/3_binary64_1509` `exp-to-pow_binary64_1504` `pow-base-1_binary64_1502` `unpow0_binary64_1501` `unpow-1_binary64_1499` `exp-lft-cube_binary64_1498` `exp-lft-sqr_binary64_1497` `exp-cbrt_binary64_1496` `exp-sqrt_binary64_1495` `div-exp_binary64_1493` `rec-exp_binary64_1492` `prod-exp_binary64_1491` `exp-diff_binary64_1490` `exp-neg_binary64_1489` `exp-sum_binary64_1488` `e-exp-1_binary64_1487` `exp-1-e_binary64_1485` `exp-0_binary64_1484` `rem-log-exp_binary64_1483` `rem-exp-log_binary64_1482` `cube-neg_binary64_1469` `rem-3cbrt-rft_binary64_1468` `sqr-neg_binary64_1456` `/-rgt-identity_binary64_1433` `-rgt-identity_binary64_1432` `-lft-identity_binary64_1431` `remove-double-neg_binary64_1430` `--rgt-identity_binary64_1428` `+-lft-identity_binary64_1426` `mul0-rgt_binary64_1425` `mul0-lft_binary64_1424` `div0_binary64_1423` `*-inverses_binary64_1422` `+-inverses_binary64_1421` `lft-mult-inverse_binary64_1420` `rgt-mult-inverse_binary64_1419` `remove-double-div_binary64_1418` `difference-of-sqr--1_binary64_1413` `difference-of-sqr-1_binary64_1412` `distribute-rgt1-in_binary64_1398` `distribute-lft1-in_binary64_1397` `associate-/l/_binary64_1389` `associate--r-_binary64_1381` `associate--l-_binary64_1380`

Counts

150 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	141	2961
1	307	2921
2	857	2897
3	3543	2897
4	4855	2897
5	5063	2897

prune381.0ms (3.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	114	3	117

Error

4.7b

Counts

117 → 3

Compiler

Compiled 6703 to 4112 computations (38.7% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

13.3b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 4 (*.f64 p p))))
13.3b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))
27.4b	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 4 (*.f64 p p)))) 3))
27.4b	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 4 (*.f64 p p)))) 3))

rewrite380.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Error

4.7b

Rules

36×	`cbrt-prod_binary64_1473`
18×	`add-sqr-sqrt_binary64_1464` `sqrt-prod_binary64_1458`
16×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
12×	`unpow-prod-down_binary64_1521` `cube-prod_binary64_1470`
8×	`sqrt-div_binary64_1459`
6×	`pow1_binary64_1503`
4×	`add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `flip3-+_binary64_1445` `cube-div_binary64_1471` `cbrt-div_binary64_1474` `flip-+_binary64_1416`
2×	`pow1/3_binary64_1524` `unpow3_binary64_1508` `cube-mult_binary64_1472` `sqr-pow_binary64_1414` `rem-cbrt-cube_binary64_1466` `pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455`

Counts

4 → 88

Calls

4 calls:

8.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 4 (*.f64 p p)))) 3))
7.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 4 (*.f64 p p)))) 3))
5.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 4 (*.f64 p p))))
5.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))

Compiler

Compiled 6166 to 3799 computations (38.4% saved)

series1.1s (9.7%)

Error

4.7b

Counts

4 → 76

Calls

4 calls:

231.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 4 (*.f64 p p))))
231.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 (*.f64 p p) 4)))
221.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 4 (*.f64 p p)))) 3))
210.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 4 (*.f64 p p)))) 3))

Compiler

Compiled 9804 to 7043 computations (28.2% saved)

simplify166.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

581×	`associate-l_binary64_1383`
487×	`associate-r_binary64_1382`
408×	`distribute-rgt-neg-in_binary64_1400`
378×	`distribute-lft-neg-in_binary64_1399`
235×	`times-frac_binary64_1448`
223×	`distribute-neg-frac_binary64_1406`
174×	`associate-/l*_binary64_1387`
151×	`div-sub_binary64_1447`
127×	`cancel-sign-sub-inv_binary64_1408`
112×	`associate-/r*_binary64_1386`
111×	`*-commutative_binary64_1373`
102×	`sub-neg_binary64_1435` `unswap-sqr_binary64_1410`
99×	`sqr-pow_binary64_1414`
80×	`neg-sub0_binary64_1437`
74×	`neg-mul-1_binary64_1438`
61×	`associate-*l/_binary64_1385`
58×	`cube-prod_binary64_1470`
52×	`distribute-lft-neg-out_binary64_1401`
48×	`associate-*r/_binary64_1384`
47×	`unpow3_binary64_1508`
42×	`distribute-rgt-in_binary64_1392` `+-commutative_binary64_1372`
36×	`distribute-lft-in_binary64_1391`
35×	`rem-sqrt-square_binary64_1455`
33×	`pow-plus_binary64_1505`
32×	`distribute-rgt-neg-out_binary64_1402`
27×	`cube-mult_binary64_1472`
23×	`cube-unmult_binary64_1479`
21×	`associate-+r-_binary64_1376`
19×	`log-prod_binary64_1528` `+-rgt-identity_binary64_1427` `associate-+l-_binary64_1377`
18×	`exp-prod_binary64_1494` `swap-sqr_binary64_1409`
17×	`distribute-rgt-out--_binary64_1396` `associate-+l+_binary64_1375`
15×	`associate-/r/_binary64_1388`
13×	`unsub-neg_binary64_1436` `associate--l+_binary64_1379` `associate-+r+_binary64_1374`
11×	`sub0-neg_binary64_1429` `pow-sqr_binary64_1415` `distribute-neg-in_binary64_1403`
10×	`rem-cbrt-cube_binary64_1466` `distribute-rgt-out_binary64_1395`
9×	`difference-of-squares_binary64_1411`
8×	`rem-square-sqrt_binary64_1454`
5×	`log-pow_binary64_1531` `associate--r+_binary64_1378`
4×	`unpow2_binary64_1507` `cancel-sign-sub_binary64_1407`
3×	`distribute-lft-out--_binary64_1394`
2×	`unpow1/2_binary64_1506` `unpow1_binary64_1500` `cube-div_binary64_1471` `distribute-frac-neg_binary64_1405` `distribute-neg-out_binary64_1404`
1×	`1-exp_binary64_1486` `rem-3cbrt-lft_binary64_1467` `rem-cube-cbrt_binary64_1465` `sqr-abs_binary64_1457` `mul-1-neg_binary64_1434` `distribute-lft-out_binary64_1393` `count-2_binary64_1390`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64_1705` `erf-erfc_binary64_1704` `erf-odd_binary64_1703` `if-if-and-not_binary64_1702` `if-if-and_binary64_1701` `if-if-or-not_binary64_1700` `if-if-or_binary64_1699` `if-not_binary64_1698` `if-same_binary64_1697` `if-false_binary64_1696` `if-true_binary64_1695` `not-gte_binary64_1694` `not-lte_binary64_1693` `not-gt_binary64_1692` `not-lt_binary64_1691` `gte-same_binary64_1690` `lte-same_binary64_1689` `gt-same_binary64_1688` `lt-same_binary64_1687` `sinh---cosh_binary64_1634` `sinh-+-cosh_binary64_1633` `sinh-cosh_binary64_1632` `tanh-def-c_binary64_1631` `tanh-def-b_binary64_1630` `tanh-def-a_binary64_1629` `cosh-def_binary64_1628` `sinh-def_binary64_1627` `tan-neg_binary64_1574` `cos-neg_binary64_1573` `sin-neg_binary64_1572` `tan-0_binary64_1571` `cos-0_binary64_1570` `sin-0_binary64_1569` `hang-m-tan_binary64_1568` `hang-p-tan_binary64_1567` `hang-m0-tan_binary64_1566` `hang-p0-tan_binary64_1565` `hang-0m-tan_binary64_1564` `hang-0p-tan_binary64_1563` `tan-+PI/2_binary64_1562` `tan-+PI_binary64_1561` `tan-PI_binary64_1560` `tan-PI/3_binary64_1559` `tan-PI/4_binary64_1558` `tan-PI/6_binary64_1557` `cos-+PI/2_binary64_1556` `cos-+PI_binary64_1555` `cos-PI_binary64_1554` `cos-PI/2_binary64_1553` `cos-PI/3_binary64_1552` `cos-PI/4_binary64_1551` `cos-PI/6_binary64_1550` `sin-+PI/2_binary64_1549` `sin-+PI_binary64_1548` `sin-PI_binary64_1547` `sin-PI/2_binary64_1546` `sin-PI/3_binary64_1545` `sin-PI/4_binary64_1544` `sin-PI/6_binary64_1543` `sub-1-sin_binary64_1542` `sub-1-cos_binary64_1541` `-1-add-sin_binary64_1540` `-1-add-cos_binary64_1539` `1-sub-sin_binary64_1538` `1-sub-cos_binary64_1537` `cos-sin-sum_binary64_1536` `log-E_binary64_1532` `log-rec_binary64_1530` `log-div_binary64_1529` `pow-base-0_binary64_1526` `unpow1/3_binary64_1509` `exp-to-pow_binary64_1504` `pow-base-1_binary64_1502` `unpow0_binary64_1501` `unpow-1_binary64_1499` `exp-lft-cube_binary64_1498` `exp-lft-sqr_binary64_1497` `exp-cbrt_binary64_1496` `exp-sqrt_binary64_1495` `div-exp_binary64_1493` `rec-exp_binary64_1492` `prod-exp_binary64_1491` `exp-diff_binary64_1490` `exp-neg_binary64_1489` `exp-sum_binary64_1488` `e-exp-1_binary64_1487` `exp-1-e_binary64_1485` `exp-0_binary64_1484` `rem-log-exp_binary64_1483` `rem-exp-log_binary64_1482` `cube-neg_binary64_1469` `rem-3cbrt-rft_binary64_1468` `sqr-neg_binary64_1456` `/-rgt-identity_binary64_1433` `-rgt-identity_binary64_1432` `-lft-identity_binary64_1431` `remove-double-neg_binary64_1430` `--rgt-identity_binary64_1428` `+-lft-identity_binary64_1426` `mul0-rgt_binary64_1425` `mul0-lft_binary64_1424` `div0_binary64_1423` `*-inverses_binary64_1422` `+-inverses_binary64_1421` `lft-mult-inverse_binary64_1420` `rgt-mult-inverse_binary64_1419` `remove-double-div_binary64_1418` `difference-of-sqr--1_binary64_1413` `difference-of-sqr-1_binary64_1412` `distribute-rgt1-in_binary64_1398` `distribute-lft1-in_binary64_1397` `associate-/l/_binary64_1389` `associate--r-_binary64_1381` `associate--l-_binary64_1380`

Counts

164 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	141	3414
1	307	3374
2	857	3350
3	3543	3350
4	4855	3350
5	5063	3350

prune447.0ms (3.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	126	3	129

Error

4.7b

Counts

129 → 3

Compiler

Compiled 7726 to 4821 computations (37.6% saved)

regimes841.0ms (7.2%)

Accuracy

Total 0.0b remaining (0.5%)

Threshold costs 0.0b (0.5%)

Compiler

Compiled 10621 to 7917 computations (25.5% saved)

bsearch4.0ms (0%)

Compiler: Compiled 12 to 9 computations (25% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64_1373`
2×	`+-commutative_binary64_1372`
1×	`1-exp_binary64_1486`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `if-if-and-not_binary64_1702` `if-if-and_binary64_1701` `if-if-or-not_binary64_1700` `if-if-or_binary64_1699` `if-not_binary64_1698` `if-same_binary64_1697` `if-false_binary64_1696` `if-true_binary64_1695` `tan-0_binary64_1571` `cos-0_binary64_1570` `sin-0_binary64_1569` `unpow1_binary64_1500` `e-exp-1_binary64_1487` `exp-1-e_binary64_1485` `exp-0_binary64_1484` `sqr-abs_binary64_1457` `sqr-neg_binary64_1456` `neg-mul-1_binary64_1438` `neg-sub0_binary64_1437` `unsub-neg_binary64_1436` `sub-neg_binary64_1435` `mul-1-neg_binary64_1434` `/-rgt-identity_binary64_1433` `-rgt-identity_binary64_1432` `-lft-identity_binary64_1431` `remove-double-neg_binary64_1430` `sub0-neg_binary64_1429` `--rgt-identity_binary64_1428` `+-rgt-identity_binary64_1427` `+-lft-identity_binary64_1426` `cancel-sign-sub-inv_binary64_1408` `cancel-sign-sub_binary64_1407` `distribute-neg-frac_binary64_1406` `distribute-frac-neg_binary64_1405` `distribute-neg-out_binary64_1404` `distribute-neg-in_binary64_1403` `distribute-rgt-neg-out_binary64_1402` `distribute-lft-neg-out_binary64_1401` `distribute-rgt-neg-in_binary64_1400` `distribute-lft-neg-in_binary64_1399`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	67
1	34	67
2	33	67

end0.0ms (0%)

sample2.5s (21.2%)

Algorithm

1×

intervals

Results

335.0ms	6120×	body	128	valid
212.0ms	754×	body	2048	valid
141.0ms	8000×	pre	128	true
112.0ms	502×	body	1024	valid
101.0ms	275×	body	4096	valid
38.0ms	226×	body	512	valid
13.0ms	123×	body	256	valid

Compiler

Compiled 1515 to 1124 computations (25.8% saved)

Details

analyze1.0s (8.6%)

sample42.0ms (0.4%)

simplify10.0ms (0.1%)

prune3.0ms (0%)

localize14.0ms (0.1%)

rewrite192.0ms (1.6%)

series974.0ms (8.3%)

simplify127.0ms (1.1%)

prune171.0ms (1.5%)

localize19.0ms (0.2%)

rewrite200.0ms (1.7%)

series1.1s (9.3%)

simplify113.0ms (1%)

prune291.0ms (2.5%)

localize34.0ms (0.3%)

rewrite277.0ms (2.4%)

series1.1s (9.5%)

simplify150.0ms (1.3%)

prune381.0ms (3.3%)

localize31.0ms (0.3%)

rewrite380.0ms (3.3%)

series1.1s (9.7%)

simplify166.0ms (1.4%)

prune447.0ms (3.8%)

regimes841.0ms (7.2%)

bsearch4.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.5s (21.2%)

Profiling